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Explore the first lecture in a series on polyhedral geometry algorithms, covering both theoretical foundations and practical applications. Delve into rational polyhedra, their projections, and various representation conversions. Learn about lattice points in rational polyhedra, including existence verification, counting methods, and description techniques with special focus on parametric polyhedra. Understand how quantifier elimination applies to optimizing compilers when working with rational and lattice polyhedra. This 1-hour 27-minute lecture was recorded during the "Francophone Computer Algebra Days" on March 12, 2025, at the Centre International de Rencontres Mathématiques in Marseille, France. Access this and other mathematical talks through CIRM's Audiovisual Mathematics Library, featuring helpful navigation tools like chapter markers, keywords, abstracts, bibliographies, and multi-criteria search functionality.
